
the commuting graph, \(\mathop {\mathrm {Com}}(G)\) , first defined by Brauer and
Fowler [1]},
in which two elements \(x\)  and \(y\)  are joined if they commute;

the enhanced power graph, \(\mathop {\mathrm {EPow}}(G)\) , first introduced by
Aalipour et al. [2]}, in which \(x\)  and \(y\)  are joined if they
generate a cyclic subgroup of \(G\) .

